Question

If V is the volume of a cuboid of dimensions a,b,c and S is its surface area then prove that 1/V=2/S(1/a +1/b+ 1/c).

Answer 1

Hey Mate !!

Here is your solution :

Given,

Dimensions = a , b and c.

=> Volume of cuboid = l × b × h

=> V = abc ------------ ( 1 )

And ,

=> Surface area of cuboid = 2 ( lb + bh + lh )

=> S = 2 ( ab + bc + ac ) --------- ( 2 )

By dividing ( 2 ) by ( 1 ) ,

=> S/V = 2 ( ab + bc + ac ) ÷ abc

=> S/V = ( 2ab + 2bc + 2ac ) ÷ abc

=> S/V = ( 2ab ÷ abc ) + ( 2bc ÷ abc ) + ( 2ac ÷ abc )

=> S/V = ( 2/c ) + ( 2/a ) + ( 2/b )

Taking out 2 as common in R.H.S,

=> S/V = 2 { ( 1/c ) + ( 1/a ) + ( 1/b ) }

Rearranging the terms ,

=> S/V = 2 { ( 1/a ) + ( 1/b ) + ( 1/c ) }

=> 1/V = ( 2/S ) { ( 1/a ) + ( 1/b ) + ( 1/c ) }

★ Proved ★

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Hope it helps !! ^_^